The function you're working with is $y = |x + 3|$, which is an absolute value function. Here's a step-by-step guide to its graph:

1. Understanding the Absolute Value: The absolute value function, $y = |f(x)|$, takes the output of $f(x)$ and makes it non-negative. In this case, $f(x) = x + 3$, so the function is the absolute value of $x + 3$.

2. Vertex: The function $y = |x + 3|$ has its vertex where the expression inside the absolute value equals zero. So, solve for $x + 3 = 0$, which gives $x = -3$. Therefore, the vertex is at $(-3, 0)$.

3. Behavior of the Graph:

   • For $x \geq -3$, the graph follows the line $y = x + 3$.
   • For $x < -3$, the graph follows the line $y = -(x + 3)$, which simplifies to $y = -x - 3$.

4. Shape of the Graph: The graph forms a "V" shape with the vertex at $(-3, 0)$, and the arms of the "V" have slopes of 1 (to the right of $x = -3$) and -1 (to the left of $x = -3$).

I can generate the graph of this function for you—just let me know if you'd like that!

Would you like further details, or do you have any other questions?

Here are some related questions you might find interesting:

1. How does changing the sign of the term inside the absolute value (like $|x - 3|$) affect the graph?
2. How do absolute value functions behave when combined with other transformations, such as vertical or horizontal shifts?
3. What is the graph of $y = |x + 3| - 2$ like, and how does it differ from the original graph?
4. How would you graph $y = |x + 3|$ using a table of values?
5. How does the absolute value function behave for large positive and negative $x$-values?

Tip: When graphing absolute value functions, always look for the vertex (where the inside expression equals zero) and use the properties of the lines on either side of the vertex to complete the graph!